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SUMMARY Stjernfelt's ''Diagrammatology'' is an investigation into the ontological foundations of semiotics. On the basis of his interpretations of Peirce and Husserl, Stjernfelt promises no less than a ''counterrevolution in semiotics'' (ix): conventionalist approaches that privilege the linguistic sign are to give way to a ''semiotic realism'' (ix). He proposes to fulfill this ''foundational task'' (ix) by inquiring into the ''phenomenological prerequisites to sign use'' (ix), and diagrams are the type of sign that provides the key to these prerequisites: Diagrams can make the a priori structures of ontological domains explicit.

The first part of the work offers an interpretation of Peirce with a focus on his ''doctrine of diagrammatical reasoning'' (xiv) and an interpretation of Husserl. Stjernfelt's aim is to highlight hitherto overlooked parallels between these two authors, in particular between Husserl's notion of ''categorial intuition'' in the ''Logische Untersuchungen'' and Peirce's conception of the epistemological function of diagrams.

The second part (chapters 9 – 18) of ''Diagrammatology'' investigates the role of diagrammatic reasoning in biosemiotics, visual studies and literary theory. These case studies are examples of the type of semiological analysis Stjernfelt seeks to establish; they can also be seen as a demonstration of the scope of the semiological analyses envisaged by the author.

The overall structure of the book is the following: In chapters 1 to 4 Stjernfelt introduces his reading of Peirce, chapter 5 explores the notion of transformation in semiotics, chapters 6 to 8 focus on Husserl and his relation to Peirce; chapters 9 – 12 are devoted to biosemiotics, chapters 13-15 present Stjernfelt's contribution to visual studies, and chapters 16-18 his take on the interpretation of literature. The blocks of chapters and some of the chapters themselves are relatively self-contained; a useful summary (xv-xix) and a diagram showing the structure of the book (xx) can be found in the Introduction.

The theoretical core of Stjernfelt's ''Diagrammatology'' is his reading of Peirce: His aim is to establish a connection between a metaphysical idea (the idea of ''real possibilities''), a semiotic position (iconicity and thereby similarity as the basic semiotic relation), and an epistemological model (Peirce's triad of abduction-deduction-induction). Diagrams play a role on all three levels: as structures of real and fictional worlds, as physical tokens of sign types, and as ''subjective representations'' (334). The correspondences between these three levels of analysis are what makes diagrams such powerful instruments of cognition. Many diagrams show explicitly the structures that other semiotic processes are implicitly based on. This is why, for Stjernfelt, the diagram can be seen as the paradigmatic sign.

The first chapter of the book outlines Peirce's ''philosophy of continuity'' (5): Peirce argues for the ''ineradicability of continuity in experience'' (6) and that is - for Stjernfelt - the (metaphysical) key to our ability to use truly general concepts, and thereby to a realist semiotics. Only insofar as reality is experienced as continuous are we capable of using signs that refer not only to extensionally defined collections of objects, but to the realm of possibility. This idea is pursued in the second chapter, where Stjernfelt states that the generalities we note, such as e.g. ''relations, tendencies, patterns, laws, dispositions'' (47) etc. are to be understood as ''real possibilities'' (46), in other words, referring to the structural or causal characteristics of a given (ontological) domain.

Chapter two also presents Peirce's well known classification of signs and connects the metaphysical and semiotic level of the analysis. Here, Stjernfelt introduces two ideas that are of central importance for a realist semiotics: Firstly, the idea that ''any higher sign, index and symbol alike, must contain, or, by association or inference terminate in, an icon.'' (29); in some respect, every sign is connected to similarity relations. Secondly, ''the icon, while not in itself general, is the bearer of a potential generality'' (29); in other words: icons are not simply mirrors of what there is, they also show (real) possibilities (and, as Stjernfelt will add later in the book, icons can only show what is possible, not what is impossible (87)).

Chapter three defends the assumption that similarity plays a foundational role in semiotics against Goodman and Eco. Chapter three is an attempt to invalidate conventionalist accounts in semiotics: In particular, Stjernfelt tries to counter every single one of Goodman's ''Seven Strictures on Similarity''. One of Stjernfelt's main concerns in this context is that to count as an icon ''a sign must signify through its similarity to its object'' (50), not simply be similar to it – the foundational task fulfilled by the icon and the distinction between icon, symbol and index as different types of reference is – among many other things – what Goodman is supposed to have failed to understand (54).

Chapter four explores the ''potential generality'' of the icon by introducing what Stjernfelt calls an ''operational'' definition of similarity (90) and thereby of the icon (91): ''the decisive test for its iconicity rests in whether it is possible to manipulate the sign so that new information as to its object appears'' (90). This extension of the notion of similarity is based on the idea of the diagram as the prototypical icon: the diagram is an icon that can be manipulated, as, for example, in geometrical proofs. Stjernfelt chooses the geometrical proof of the Pythagorean theorem (x sq.) as an example to explain his notion of ''operational'' similarity: the manipulation of the diagram in a space conceived as continuous gives rise not only to a new insight, but to a general proposition, a law. Diagrams are representations of ''rationally related objects'' (94). Stjernfelt extends this model to all icons and, thereby, to (elements in) all sign use. ''[D]iagram experimentation'' - i.e. ''various counterfactual transformations of the phenomenon's real possibilities as the means of gaining insight into it'' (116) - is a ''basic rational semiotic behaviour'' (115) present in semiotic processes as different as ''the tropisms studied by biosemiotics, the contemplation of pictures, metaphorical, analogical, and poetical reasoning, linguistic and analogical syntax, basic sensorymotor schemata, as well as mathematics proper'' (115). For Stjernfelt, this idea is ''the core point of Peircian diagrammatology'' (99).

Chapter five adds historical perspective to this idea by presenting transformation as a central category in semiotics. Stjernfelt traces the notion of transformation in Lévi-Strauss, Thom, Greimas, and others, and in contemporary works in Cognitive Linguistics.

Chapters six to eight turn to Husserl and Stjernfelt's reading of the phenomenological aspects of diagrammatology. Categorial intuitions in Husserl's ''Logische Untersuchungen'' play, according to Stjernfelt, a role that is ''analogous'' to diagrams in Peirce (158): both permit abstraction by something like eidetic variation, and ''both point to the necessity of the direct intuitive access to ideal objects as a prerequisite to a phenomenologically perceived realism'' (159).

Both, intuition and variation are needed to support Stjernfelt's ''non-inductive'' (137) explanation of abstraction, an abstraction that yields the results demanded by the author: nothing less than a ''formal ontology'' (162) that takes its cue from Husserl's mereological analyses. Diagrams make formal ontological structures explicit: the structure of the diagram may show the mereological structure of the domain represented (173). Chapter 8 traces these ontological claims back to an ''Austrian idea of the a priori'' (175) (shared by Brentano and his disciples, Husserl among them). These authors had, according to Stjernfelt, a realist conception of the a priori: a priori structures are shared by propositions and states-of-affairs, and are not the result of a constitution of the object by a Kantian subject (176).

Diagrams are in this perspective a ''royal road to the investigation of the synthetic a priori'' (192); but – as Stjernfelt notes – the problem remains ''where [...] the precise borderline [is] between the synthetic a priori laws of a given domain on the one hand, and the contingent, empirical data and tendencies recorded in that domain, on the other '' (192). Stjernfelt holds that this question can only be addressed by analyzing specific domains – and the remaining chapters of the book do just that: they present three exemplary domains of investigation in a digrammatological perspective (see 193).

Chapters nine to twelve are devoted to biosemiotics. Biosemiotics claims the ''fundamentally semiotic character of biological processes'' (257) and extends the range of semiotics far beyond the range of human behavior. For biosemiotics semiotic processes are embodied: any type of categorial perception is seen as a semiotic process. Stjernfeld cites von Uexküll's tick as an example: every organism forms a functional circle with its environment and its interactions with this environment are interpreted as semiotic processes by biosemiotics.

In this context, an important task for semiotics is to draw up a ''semiotical ladder of evolution'' that establishes correlations between ''basic body types'' and ''semiotic ability'' (273). Stjernfelt proposes a first draught for such a ''biosemiotic Scala Naturae'' (272), that notes, for example, that it is not the use of symbols as such, but ''hypostatic abstraction'' (254) – the ''possibility of making an operation into the object of a new operation'' (251) – that is typical for (but not exclusive to) human beings.

Chapters 13 to 15 apply ''diagrammatological'' ideas to the domain of visual studies. Stjernfelt opts for a conception of ''picture'' that is as broad as his definition of iconicity – it includes non-visual pictures (he thinks of sounds ''picturing'' each other) and ''natural'' pictures such as mirror images (275). For Stjernfelt, not surprisingly, pictures are defined by similarity (276): all pictures are ''also'' diagrams or maps (279). By consequence, all pictures must be representational: every picture represents something, but not necessarily a material object – some pictures represent emotions or ideas (276). Twentieth century art, far from being non-representational, is a ''triumph of similarity'' (277).

Stjernfelt gives two elaborate examples for a diagrammatical analysis of pictures. The first is the interpretation of an altarpiece depicting the Last Supper by the Danish painter C.W. Eckersberg. Stjernfelt bases his description on an interpretation by Erik Fischer who noted that one place at the table is conspicuously empty - that of Judas. Fischer takes the empty wooden stool in the foreground as the starting point of his interpretation. The perspectival horizon constructed from the stool is different from the horizon constructed from architectural elements (in particular the room's ceiling). Judas' horizon is lower than that of the rest of the piece, which is dominated by the figure of Christ in the middle. Stjernfelt concludes that there is a ''deliberate use of double perspective with the rhetorical effect of a structural derogation of Judas'' (282).

The interpretation of the altarpiece is supposed to demonstrate two ideas: Firstly, that the diagrammatic interpretation of pictures follows a general pattern of reasoning that can be described in Peircean terms: ''This presentation demonstrates the characteristic shifting between abduction understood as qualified guesses faced with strange observations, deduction understood as diagram experimentation on the picture, abductive helping hypotheses, inductive probability arguments and a final conclusion measured on the symbolical governing of the diagram'' (285). Secondly, the interpretation of the painting is supposed to demonstrate that the ''logical aspects of pictures'' depend on their very iconicity (285) – the unity of these two aspects is what the diagram ultimately reveals.

Stjernfelt's second example is Malevich's ''Suprematist Composition: White Square on White''. Diagram manipulation in a case like this would consist in imagining variations, e.g. imagining a different size or position for the inner square (see 286). The difference between the Malevich and the first example is the ''radical underdetermination'' (288) of the former, typical for twentieth century art.

In chapter 14, Stjernfelt turns again to the spatial order of pictures. He distinguishes two types of pictures, based loosely on Husserl's reflections on imaginative acts: one type of picture allows the viewer to construct its space as accessible, as if the viewer could enter into the picture and move around in the constructed space. The prototype of that kind of picture would be a landscape painting. The prototype for the second type of picture, the inaccessible picture, would be a portrait. Stjernfelt suggests that accessibility could be crucial for the atmosphere of a picture (see 310).

Chapter 15 presents an outline of a theory of the sketch, and its relation to the diagram. Sketches may be diagrams or proto-diagrams or neither (like the artistic sketch, which is characterized by the indeterminacy typical for some works of art).

In chapters 16 to 18 Stjernfelt turns to literary studies. He reconstructs literary interpretation in Peircian terms, i.e. as an interplay between abduction, deduction and induction (see 328), and follows Ingarden in his distinction of levels of interpretation (chapter 17). Chapter 18 offers a final case study, an analysis of the spy novel, in order to demonstrate the iconic relation of ''conceptual schemata in literary semantics'' and the ''regional ontology'' of the world of espionage (365). Features of the regional ontology would be ''iconically reproduced'' (382) in the novel; for example, ''a tendential structural difference between foreign and domestic service'' (382) or ''the positional character of the spy – the possession of secret knowledge as determination independent of any espionage intention or affiliation of the person in question''(382).

EVALUATION Stjernfelt's ''Diagrammatology'' is an ambitious book: its main subject is the foundation of semiotics, but it can also be read as a contribution to the study of diagrams, to the interpretation of Peirce, Husserl, and a great number of other authors, to biosemiotics, and to visual and literary studies. Specialists in any of these areas will find the relevant chapters an interesting read, even if Stjernfelt rarely refers to the literature in the respective disciplines and leaves it to the reader to situate his approach within the field. The book's thematic richness is an asset, but also a liability – the author's efforts to cover the entire domain of semiotics lets the reader sometimes lose sight of the main argument. Not all of Stjernfelt's arguments are equally clear and he does not always entirely avoid polemics. Also, as is almost unavoidable in a book of this scope, there are loose threads. (The most puzzling of these is in the chapter on biosemiotics where Stjernfelt says that ''hypostatic abstraction seems restricted to mankind, even if maybe unevenly distributed among us (which might in fact be an indication that selection pressure for it is still at work, or has been until recently).'' (254). This is a very strange thing to say and would certainly require some explanation.)

Opinions will be divided on Stjernfelt's contribution to the foundation of semiotics. Those convinced of the necessity of a ''foundational task'' for semiotics and those leaning towards a semiotic realism will welcome Stjernfelt's approach. All others will probably remain unconvinced: Stjernfelt's arguments against Goodman's ''Seven Strictures on Similarity'' are mostly begging the question (and Stjernfelt himself seems to sense the problem: this is one of the chapters where his style verges at times on the polemical).

That said, ''Diagrammatology'' provides two essential leads for debates in general semiotics and in visual studies: firstly, the introduction of phenomenological problems into semiotic discussions is certainly an important contribution. Whether under the auspices of a realist or a nominalist approach, semiotics should not exclude phenomenological questions and the haunting epistemological problems this implies - in particular the problem of abstraction and the question of regional ontologies.

Stjernfelt's examples for regional ontologies suffer from the defects all descriptions of this kind will necessarily be afflicted with: they will be in part trivial, and in part contestable, because highly dependent on culture-specific parameters. His analysis of the spy novel is a case in point. In that sense, Stjernfelt is quite correct in noting that the question of the borderline between a priori and a posteriori propositions must be asked as soon as ontologies become ''regional'' (though the reviewer – being a nominalist – would suggest that the second Wittgenstein's reflections on grammatical and empirical propositions could provide a useful model). The aim to find ''real possibilities'' by recognizing similarities adds to the difficulty: in his reading of spy novels, Stjernfelt tries to identify the real life counterparts for the laws of a genre. This is arguably not the most interesting way to place semiotic practices in a real world context – audience studies or narratological analyses (in a technical sense), for example, would provide alternative accounts. And, apart from the insistence on similarities, there is no reason to ignore these accounts in the context of reflections on regional ontologies.

Stjernfelt's second major contribution to debates in general semiotics is his focus on the study of diagrams: A general semiotics that takes neither pictures nor language as the prototypical sign provides a fresh start for more specialized disciplines like visual studies. It could also help relaunch the debate on a basic methodological question in semiotics, the question whether, in a semiotic theory, there will always be one type of sign that serves (implicitly or explicitly) as the prototype for all signs in general.

Diagrams are currently rediscovered as an object of study in their own right. In this context, the notion of diagram transformation as presented in ''Diagrammatology'' could play a really important part in explaining the epistemological impact of diagram use. And Stjernfelt addresses, albeit in an indirect manner, another crucial question in diagram studies: Whether one subscribes to the metaphysical framework Stjernfelt establishes or not, his identification of logical structure and iconicity is an attempt to solve one of the most vexing problems in the study of diagrams, the question of their classification in relation to digital representations on the one hand, and analog representations, like pictures, on the other. Again, Stjernfelt offers an interesting approach to an important question, but just as his universalism takes him very far from the regional ontologies he wants to explore, his generalised idea of the diagrammatic will take him very far from the work of those in search of working definitions for specific types of representations, diagrams among them.

Stjernfelt identifies a taxonomy of diagrams as one of the future tasks for semiotics (see 111), but his extension of the scope of semiotics to the natural world and of the notion of diagram beyond even the visual makes this a daunting task indeed: In how far can his analysis of the spy novel be called diagrammatic? In how far is his interpretation of the ''Last Supper'' (that is based on a visual diagram) prototypical for visual studies – how do other aspects, from colors to social background, fit into the equation? The identification of the logic and the iconic comes at a price: the virtual impossibility to distinguish the diagrammatic from any other form of abstraction – a price the author willingly pays in the name of realist semiotics. For all those who do not share this position the question will rather be, in how far ''diagrammatology'' is a useful metaphor for the analysis of the cognitive strategies inherent in our semiotic practices.

ABOUT THE REVIEWER Elisabeth Birk has a background in philosophy and linguistics. She teaches media theory in the master's program ''Media Informatics'' at Aachen University (RWTH Aachen), Germany. She finished her PhD thesis on ''Rules and Examples. Goodman and Wittgenstein on Samples and Their Use'' in 2007. Her current research focuses on general semiotics and visual studies, in particular on questions of classification and the use of diagrams in linguistics.